The head of Addison Lee, one of the UK's biggest minicab companies, has angered cycle campaigners by describing deaths and serious injuries among inner-city cyclists as inevitable and primarily the fault of untrained riders.

John Griffin has spent several days in the spotlight after he ordered the drivers of his company's 3,500 vehicles in London to use bus lanes, which are reserved by law for buses, coaches, motorbikes and licensed black cabs, as well as cyclists.

Griffin, who views the bus lane rules as discriminatory against minicab firms, promised to indemnify his staff against any fines. Transport for London, which sets bus lane policy, warned that Addison Lee staff could lose their taxi licences for following Griffin's order.

Griffin's argument is deeply unpopular among many London cyclists, who use the bus lanes as a relatively less traffic-choked haven, particularly along major routes.

In the wake of the row – which deepened after it emerged that Griffin's firm had donated £250,000 to the Conservative party and he had discussed the issue with the then transport secretary, Philip Hammond – news began spreading of Griffin's personal view of cyclists, as expressed in the latest edition of his company's in-house magazine, Add Lib, read mainly by customers in the firm's cars.

In his chairman's column, Griffin appears to question the rights of cyclists to use London roads.

"This summer the roads will be thick with bicycles," Griffin wrote. "These cyclists are throwing themselves on to some of the most congested spaces in the world. They leap on to a vehicle which offers them no protection except a padded plastic hat.

"Should a motorist fail to observe a granny wobbling to avoid a pothole or a rain drain, then he is guilty of failing to anticipate that this was somebody on her maiden voyage into the abyss. The fact is he just didn't see her and however cautious, caring or alert he is, the influx of beginner cyclists is going to lead to an overall increase in accidents involving cyclists.

"The rest of us occupying this road space have had to undergo extensive training. We are sitting inside a protected space with impact bars and air bags and paying extortionate amounts of taxes on our vehicle purchase, parking, servicing, insurance and road tax."

He concluded: "It is time for us to say to cyclists, 'You want to join our gang, get trained and pay up'."

The article soon generated a large amount of Twitter traffic, with many pointing out that no vehicles pay "road tax". Vehicle excise duty is instead based on vehicle emissions, meaning bikes would be zero-rated even if made liable for it.

Sixteen cyclists died in London in 2011, but there is little evidence to back up Griffin's idea that poor cycling is mainly to blame. Department for Transport figures from 2009 showed that police deemed drivers solely responsible in up to 75% of accidents involving cyclists UK-wide.

Mike Cavenett, of the London Cycling Campaign, called Griffin's comments "beyond belief". He said: "Given the five people who have died on bikes in London this year, it's sickening to read an article by a company chairman which basically encourages conflict on the roads."

Griffin's attitude was deeply divisive, Cavenett said. "Cyclists are normal people … many of whom who will be his clients, or people who manage contracts with Addison Lee. Cyclists in London are Londoners, they're not some odd beast. This is what he needs to get in his head."

Chris Peck, policy co-ordinator for the countrywide cycling group CTC, said Griffin's argument about being unable to miss swerving bikes showed a worrying degree of ignorance.

"Not content with wishing to emulate cab drivers' access to bus lanes, Griffin has now provided an hilarious, though sadly not satirical, imitation of a cab driver uttering a tedious anti-cycling rant," Peck said.

"Remarkably, it seems he hasn't been reading his highway code, which states in rule 213: 'Cyclists may suddenly need to avoid uneven road surfaces and obstacles such as drain covers or oily, wet or icy patches on the road. Give them plenty of room and pay particular attention to any sudden change of direction they may need to make.'"

Peck added: "Motor vehicle users must undergo thorough training because through their poor driving hundreds of thousands of people are killed and injured each year. Cyclists do not represent such a risk and, more to the point, are, by choosing to cycle, reducing congestion and the burden of public health linked to physical inactivity and air pollution."

The row now looks set to arrive at the Addison Lee headquarters in north London: a Facebook page has been set up to organise a cyclists' "die-in" on Monday.

Addison Lee released a statement from Griffin saying he still supported compulsory training and insurance for London's cyclists. But he added: "I accept that the tone of the article was perhaps a little too inflammatory. It was meant to entertain and generate debate, but the online reaction has obscured the main message that there are many inexperienced cyclists who need better training to be safe on London's busy roads.

"Contrary to what has been reported, at no point did I suggest that motorists are never to blame. Both cyclists and motorists have a responsibility to use the roads safely."